1. Forging new generations of engineers
Free Body Diagrams
Principles of EngineeringTM
Lesson Statics
Forging new generations of engineers
Project Lead The Way, Inc.
Copyright 2007

2. Free Body Diagrams

3. Gravity Weight, W, is a force. Gravity, g, is an acceleration.
The acceleration of gravity on earth is approximately:
9.81 m/s² in SI units and
32.2 ft/s² in US Customary units.
We know from Newton’s 2nd law that
Force = mass * acceleration
F = m * a
Therefore we can write:
W = m * g

4. Gravity
The Statue of Liberty has a mass of 225,000 kg. How much does she weigh?
W = m * g
Write the formula:
Substitute known values:
W = (225,000 kg) * m/s²
Present solution with units:
W = N

5. Gravity
The Statue of Liberty weighs Newtons, which is 496,210 pounds!
If she is exerting a lb force down, the how much does Liberty Island have to push up on her to maintain static equilibrium?
lb, according to Newton’s 3rd law

6. Free-Body Diagram A scalar is simply a number, a magnitude alone.
A force is usually shown as a vector, which includes both magnitude and a direction.
Force (or free-body) diagrams show the relative magnitude and direction of all forces acting upon an object. The object must be isolated and “free” of its surroundings.

7. Free-Body Diagram
This is a free-body diagram of the Statue of Liberty. She is represented by a simple box. The forces acting on her are labeled with a magnitude and the arrow shows direction. Notice the surrounding objects are stripped away and the forces acting on the object are shown. lb

8. Free-Body Diagram
W here represents the force of the weight of the statue.
N is the normal force, which represents the force Liberty Island is pushing back up on the statue.
The island has a great resistance to compression. The ground is exerting a force upward on the statue perpendicular, or normal, to the surface. lb
N =
W =

9. Free-Body Diagram Think of the diagram on an XY plane.lb
N =
W =
(Positive y-direction) +y +x
(Positive x-direction)
Think of the diagram on an XY plane.
If “up” is assumed to be the positive direction, then N is positive and W is negative.

10. Free-Body Diagram Fy = 0 + Fy = W + Nlb
N =
W =
(Positive y-direction) +y +x
(Positive x-direction)
The first line of this calculation reads,
“The sum of the Forces in the positive y direction is W + N” (  is the Greek symbol for “sum” )
+ Fy = W + N
Fy = ( lb) + ( lb )
Fy = 0
The sum of the forces in the y is zero.
The forces acting on the object cancel each other out.

11. Static Equilibrium Review
We know F = m * a, where “a” is acceleration.
If a = 0, then F = m * 0 = 0.
When  F = 0, the object is not accelerating.
We we can then say that the forces acting on the object cancel each other out and it is in a state of static equilibrium.

12. Force/Free Body Diagrams
Create a free body diagram (FBD) for each of the following situations. Draw a FBD of the gorilla: W N
Free Body Diagram of the Sitting Gorilla (The box represents the gorilla, W = weight of the gorilla, N = Normal force)
Sitting Gorilla

13. Force/Free Body Diagrams
Create a free body diagram (FBD) for each of the following situations. Draw a FBD of the gorilla: N W
This is also an acceptable diagram.
Sitting Gorilla

14. Force/Free Body Diagrams
Draw a FBD of the wooden swing:
Free Body Diagram of the wooden swing (The box represents the wooden swing, W = weight of the swing and the parrot, T represents the ropes that are in tension supporting the weight) W T2 T1
Parrot on wooden swing hung by ropes

15. Force/Free Body Diagrams
Draw a FBD of bucket the bungee jumper leaped from: W T
Free Body Diagram of the bucket (T represents the tensile force of the cable the bucket is suspended from, and W is the weight of the diver and the bucket)
Bungee jumping from crane

16. Force/Free Body Diagrams
Draw a FBD of the ring at point C: A B C D
TCA
TCB
TCD
Free Body Diagram of the ring at point C (T represents the force of the cables that are in tension acting on the ring)
Traffic Light supported by cables

17. Force/Free Body Diagrams
Draw a FBD of the traffic light: W
TCD A B C D
Free Body Diagram of the traffic light (TCD represents the force of the cables acting on the light and W is the weight acting on the light)
Traffic Light supported by cables

18. Force/Free Body Diagrams
Draw a FBD of the pin at point A: A B E D C
TAE
TAC
TAB
TAD
Free Body Diagram of pin A
(If you consider the third dimension, then there is an additional force acting on point A into the paper: The force of the beam that connects the front of the bridge to the back of the bridge.)
Pin-Connected Pratt Through Truss Bridge